He urged Khartoum to dwell on the full implementation of the signed cooperation agreements reached last year.
The SPLM-North, made up of fighters who sided with the South during the civil war, controls part of the Sudan side of the border, which complicates setting up the buffer zone.
“In the name of the President and in the name of the Republic of South Sudan that we are not training any rebel from Southern Kordofan or Southern Blue Nile,” Dr. Marial said.
The two countries had repeatedly accused each other of supporting militia to fight against the other.
The nations failed to fully implement the cooperation agreement brokered by the African Union believed to be the catalyst for peace and stability between the two countries.
Sudan and South Sudan failed to agree on how to withdraw armies from their disputed border after a round of talks in Ethiopia, delaying again the resumption of crucial oil exports.
The two neighbours came close to war in April 2012 in the worst border clashes since South Sudan seceded from Sudan in 2011 under a 2005 deal which ended decades of civil war.
After mediation from the African Union, both countries agreed in September to set up a demilitarized buffer zone and resume oil exports from landlocked South Sudan through Sudan. Oil is vital to both economies.
But neither side withdrew its army from the 2,000-km (1,200-mile) border due to mistrust left from one of Africa’s longest civil wars.